Numerical Solution of Stochastic Differential Equations with Jumps in Finance

Prof. Eckhard Platen holds the Chair in Quantitative Finance at the University of Technology, Sydney. Author of books on numerical methods for stochastic differential equations and recent book on benchmark approach at Springer Verlag. Has written more than 140 papers in finance, insurance and applied mathematics and serves on the editorial boards of five international journals including Mathematical Finance and Quantitative Finance

From the reviews: "The book is accessible at a graduate student level, though some parts of the book are more advanced. It can also be used by readers with enough mathematical background as a reference book for methods and techniques on numerical approximations of SDEs. ... contains an extensive up-to-date bibliography, including bibliographic notes for each chapter, making it an excellent reference source on numerical solutions of SDEs with jumps. The book is very well written and can be used as a textbook for a graduate level course." (Igor Cialenco, Mathematical Reviews, Issue 2012 b) "This research monograph by Eckhard Platen and Nicola Bruti-Liberati gives a comprehensive account of the theory of numerical approximation of solutions of stochastic differential equations driven by jump processes. ... The material is supplemented by a large number of exercises. The underlying principles are carefully explained and well motivated by the authors. ... I enjoyed very much the lucid and clear writing style of the exposition in combination with many interesting examples from mathematical finance." (H. M. Mai, Zentralblatt MATH, Vol. 1225, 2012)

• Stochastic Differential Equations with Jumps.- Exact Simulation of Solutions of SDEs.- Benchmark Approach to Finance and Insurance.- Stochastic Expansions.- to Scenario Simulation.- Regular Strong Taylor Approximations with Jumps.- Regular Strong Itô Approximations.- Jump-Adapted Strong Approximations.- Estimating Discretely Observed Diffusions.- Filtering.- Monte Carlo Simulation of SDEs.- Regular Weak Taylor Approximations.- Jump-Adapted Weak Approximations.- Numerical Stability.- Martingale Representations and Hedge Ratios.- Variance Reduction Techniques.- Trees and Markov Chain Approximations.- Solutions for Exercises.